$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x + 1$ and $ BC = 9x - 6$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x + 1} = {9x - 6}$ Solve for $x$ $ -x = -7$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({7}) + 1$ $ BC = 9({7}) - 6$ $ AB = 56 + 1$ $ BC = 63 - 6$ $ AB = 57$ $ BC = 57$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {57} + {57}$ $ AC = 114$